Math Problem Statement
7,20,47,94
Solution
The given sequence is: 7, 20, 47, 94.
To find the next term or a pattern in this sequence, let's first analyze the differences between consecutive terms:
We observe that the differences are increasing in a specific pattern. Let's examine the differences between these differences:
So, the differences themselves are increasing by 6 each time (14, 20,...). If this pattern continues, the next difference should be:
Therefore, the next term in the sequence is:
The next term in the sequence is 167.
Would you like a detailed explanation or further analysis on this sequence?
Here are some related questions you might consider:
- Can we derive a general formula for this sequence?
- What kind of sequence is this (e.g., arithmetic, quadratic)?
- How does finding second differences help identify patterns in sequences?
- What is the importance of higher-order differences in sequence analysis?
- Can this pattern be modeled by a polynomial equation?
Tip: When analyzing number sequences, checking differences and second differences often helps detect hidden patterns.
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequences
Higher-Order Differences
Formulas
Difference of Consecutive Terms Formula
Higher-Order Difference Pattern
Theorems
Sequence Difference Theorem
Suitable Grade Level
Grades 7-10